Title: Valid inferential models and conformal prediction.
Abstract: Given an exchangeable data sequence, which may include covariates, the goal is to quantify uncertainty about the next observable using a probabilistic predictor, for example, a predictive distribution or perhaps a non-additive lower/upper probability. Here I'll define what it takes for a probabilistic predictor to be "valid" and discuss certain consequences of that definition, in particular, that validity and additivity are apparently incompatible. Next I'll construct an inferential model, whose corresponding probabilistic predictor is a possibility measure, show that it satisfies the validity property, and draw connections to Vovk et al's conformal prediction method. Illustrations will be given and, if time allows, I'll discuss a subtle detail underlying the important special case of classification.
This talk is based largely on joint work with Leonardo Cella in the following paper (and some recent follow ups):
Bio: Dr. Ryan Martin is a Professor in the Department of Statistics at North Carolina State University. His research interests include asymptotics, empirical Bayes analysis, high- and infinite-dimensional inference problems, foundations of statistics, and imprecise probability. He is co-author of the monograph Inferential Models and co-founder of the Researchers.One online platform that promotes open communication of scientific research and other scholarly work.